Well-posedness and exponential stability for coupled Lamé system with viscoelastic term and strong damping

2018 ◽  
Vol 75 (12) ◽  
pp. 4397-4404 ◽  
Author(s):  
Abderrahmane Beniani ◽  
Noureddine Taouaf ◽  
Abbes Benaissa
Keyword(s):  
Exponential Stability ◽  
Well Posedness ◽  
Strong Damping ◽  
Lamé System ◽  
Lame System ◽  
Viscoelastic Term

scholarly journals Well-posedness and exponential stability for coupled Lamé system with a viscoelastic damping

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3591-3598
Author(s):  
Noureddine Taouaf ◽  
Noureddine Amroun ◽  
Abbes Benaissa ◽  
Abderrahmane Beniani
Keyword(s):  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Viscoelastic Damping ◽  
Well Posedness ◽  
Lamé System ◽  
Lame System

In this paper, we consider a coupled Lam? system with a viscoelastic damping in the first equation. We prove well-posedness by using Faedo-Galerkin method and establish an exponential decay result by introducing a suitable Lyaponov functional.

scholarly journals Stability result of the Lamé system with a delay term in the internal fractional feedback

2021 ◽  
Vol 13 (2) ◽  
pp. 336-355
Author(s):  
Abbes Benaissa ◽  
Soumia Gaouar
Keyword(s):  
Exponential Stability ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Stability Result ◽  
Classical Theorem ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
Lamé System ◽  
Lame System

Abstract In this article, we consider a Lamé system with a delay term in the internal fractional feedback. We show the existence and uniqueness of solutions by means of the semigroup theory under a certain condition between the weight of the delay term in the fractional feedback and the weight of the term without delay. Furthermore, we show the exponential stability by the classical theorem of Gearhart, Huang and Pruss.

Well posedness and exponential stability in a wave equation with a strong damping and a strong delay

2016 ◽  
Vol 57 (11) ◽  
pp. 111501 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Abdelfeteh Fareh ◽  
Nadjet Doudi
Keyword(s):  
Wave Equation ◽  
Exponential Stability ◽  
Well Posedness ◽  
Strong Damping

scholarly journals Well-posedness and asymptotic stability for the Lamé system with internal distributed delay

2018 ◽  
Vol 22 (1) ◽  
pp. 31-41 ◽  
Author(s):  
Noureddine Taouaf ◽  
Noureddine Amroun ◽  
Abbes Benaissa ◽  
Abderrahmane Beniani
Keyword(s):  
Asymptotic Stability ◽  
Distributed Delay ◽  
Well Posedness ◽  
Lamé System ◽  
Lame System

scholarly journals DECAY RATES FOR A COUPLED VISCOELASTIC LAMÉ SYSTEM WITH STRONG DAMPING

2020 ◽  
Vol 25 (2) ◽  
pp. 226-240
Author(s):  
Baowei Feng ◽  
Haiyan Li
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Strong Damping ◽  
Lamé System ◽  
Lame System

In [6] Beniani, Taouaf and Benaissa studied a coupled viscoelastic Lamé system with strong dampings and established a general decay result. In this paper, we continue to study the system. Assuming gi0(t) ≤−ξi(t)Hi(gi(t)), i = 1,2, we establish an explicit and general decay result, which is optimal, to the system. This result improves earlier results in [6].

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